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A sum is the result of an addition. For example, adding 1, 2, 3, and 4 gives the sum 10, written 1+2+3+4=10. (1) The numbers being summed are called addends, or sometimes ...

An algorithm which extrapolates the partial sums s_n of a series sum_(n)a_n whose convergence is approximately geometric and accelerates its rate of convergence. The ...

The reciprocal of the arithmetic-geometric mean of 1 and sqrt(2), G = 2/piint_0^11/(sqrt(1-x^4))dx (1) = 2/piint_0^(pi/2)(dtheta)/(sqrt(1+sin^2theta)) (2) = L/pi (3) = ...

Pre-Algebra

The number M_2(n) = 1/nsum_(k=1)^(n^2)k (1) = 1/2n(n^2+1) (2) to which the n numbers in any horizontal, vertical, or main diagonal line must sum in a magic square. The first ...

Kepler's equation gives the relation between the polar coordinates of a celestial body (such as a planet) and the time elapsed from a given initial point. Kepler's equation ...

Roughly speaking, isospectral manifolds are drums that sound the same, i.e., have the same eigenfrequency spectrum. Two drums with differing area, perimeter, or genus can ...

The combination of a central dilation and a rotation about the same center. However, the combination of a central dilation and a rotation whose centers are distinct is also a ...

Let s=1/(sqrt(2pi))[Gamma(1/4)]^2=5.2441151086... (1) (OEIS A064853) be the arc length of a lemniscate with a=1. Then the lemniscate constant is the quantity L = 1/2s (2) = ...

The word "harmonic" has several distinct meanings in mathematics, none of which is obviously related to the others. Simple harmonic motion or "harmonic oscillation" refers to ...